Freeform imaging lens and freeform imaging system using the same

ABSTRACT

A freeform imaging lens defined in a (x, y, z) coordinate is provided. The freeform imaging lens comprises a first surface and a second surface opposite to the first surface. The first surface comprises a first freeform surface and a second freeform surface symmetrical about x-z plane. The first freeform surface and the second freeform surface are 5 th  order xy-polynomial curve surfaces. The second surface is a 10 th  order aspheric surface. The present disclosure also relates to a freeform imaging system using the above freeform imaging lens.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims all benefits accruing under 35 U.S.C. §119 fromChina Patent Application No. 201310503691.2, filed on Oct. 24, 2013 inthe China Intellectual Property Office, disclosure of which isincorporated herein by reference.

BACKGROUND

1. Technical Field

The present disclosure relates to a freeform imaging lens and a freeformimaging system using the same.

2. Description of Related Art

Compared with conventional rotationally symmetric surfaces, freeformoptical surfaces have higher degrees of freedom, which can reduce theaberrations and simplify the structure of the system in optical design.In recent years, with the development of advancing manufacturetechnologies, freeform surfaces have been successfully used in theimaging field, such as head-mounted-displays, reflective systems,varifocal panoramic optical systems and microlens arrays.

In some related art, the freeform imaging systems cannot provide asuperior performance in imaging, and requires multi-mirrors which makesit hard to be assembled.

What is needed, therefore, is to provide a freeform imaging system, inwhich the freeform imaging system can provide a superior performance inimaging, and can be easily assembled.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of the embodiments can be better understood with referenceto the following drawings. The components in the drawings are notnecessarily drawn to scale, the emphasis instead being placed uponclearly illustrating the principles of the embodiments. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 shows a schematic structural view of one embodiment of a freeformimaging system.

FIG. 2 shows a schematic structural view of one embodiment of a freeformlens of the freeform imaging system of FIG. 1.

FIG. 3 shows an imaging result of the freeform imaging system.

FIG. 4 shows a schematic view of one embodiment of a scanning error ofthe freeform imaging system.

FIG. 5 shows a modulation transfer function (MTF) curve of oneembodiment of the freeform imaging system with a field angle of 0degree.

FIG. 6 shows a MTF curve of one embodiment of the freeform imagingsystem with a field angle of +20 degrees.

FIG. 7 shows a MTF curve of one embodiment of the freeform imagingsystem with a field angle of +40 degrees.

FIG. 8 shows a MTF curve of one embodiment of the freeform imagingsystem with a field angle of +60 degrees.

DETAILED DESCRIPTION

The disclosure is illustrated by way of example and not by way oflimitation in the figures of the accompanying drawings in which likereferences indicate similar elements. It should be noted that referencesto “an” or “one” embodiment in this disclosure are not necessarily tothe same embodiment, and such references mean at least one.

References will now be made to the drawings to describe, in detail,various embodiments of the freeform imaging system.

Referring to FIG. 1, a freeform imaging system 100 of one embodimentcomprises: a light source (not show), an entrance pupil 12, a reflector14, a freeform imaging lens 16 and an image sensing element 18. Thefreeform imaging system 100 is defined in a (x, y, z) coordinate.

The light source outputs a laser L along the y-axis. A width of thelaser L can be greater than 3 millimeters, and a wavelength of the laserL is not limited. In one embodiment, the laser L is an infrared laserwith the wavelength of about 780 nm and the width of about 3millimeters.

The entrance pupil 12 is located on a light path of the laser L andblocks excess laser L. A diameter of the entrance pupil 12 can be chosenaccording to different embodiments. In one embodiment, the diameter ofthe entrance pupil 12 is about 3 millimeters.

The reflector 14 is located on a side of the entrance pupil 12 oppositeto the light source, and perpendicular to a y-z plane. The reflector 14reflects the laser L to form a reflected light R in the y-z plane. Thereflector 14 has a center O₁ and is capable of revolving around thecenter O₁. An angle α can be formed between the reflector 14 and they-axis. The angle α can be in a range from about 15 degrees to about 75degrees.

The freeform imaging lens 16 is an f-θ lens, and is located on a lightpath of the reflected light R. The reflected light R is refracted by thefreeform imaging lens 16 to form a refracted light T. Referring to FIG.2, the freeform imaging lens 16 comprises a front surface 162 and a backsurface 164 opposite to the front surface 162. An effective clearaperture R₁ of the front surface 162 along the y-axis can be greaterthan 154.82 millimeters. In one embodiment, the effective clear apertureR₁ of the front surface 162 along the y-axis is about 154.82millimeters. An effective clear aperture R₂ of the back surface 164along the y-axis can be greater than 163.39 millimeters. In oneembodiment, the effective clear aperture R₂ of the back surface 164along the y-axis is about 163.39 millimeters.

The front surface 162 comprises a first freeform surface 1622 and asecond freeform surface 1624. The first freeform surface 1622 and thesecond freeform surface 1624 are symmetrical about x-z plane. The frontsurface 162 has a center O₂. The back surface 164 has a center O₃. Adistance between the center O₁ and the center O₂ along the y-axis isabout 42.29 millimeters. A distance between the center O₂ and the centerO₃ along the y-axis is about 44.69 millimeters. A material of thefreeform imaging lens 16 is not limited. In one embodiment, the materialof the freeform imaging lens 16 is PMMA with a refractive index of about1.4917 and an Abbe number of about 76.

The first freeform surface 1622 can be a 5^(th) order XY-polynomialcurve surface. In some embodiments, an analytic form of the firstfreeform surface 1622 satisfies:

${{z\left( {x,y} \right)} = {\frac{c_{1}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c_{1}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}y} + {A_{3}x^{2}} + {A_{5}y^{2}} + {A_{7}x^{2}y} + {A_{9}y^{3}} + {A_{10}x^{4}} + {A_{12}x^{2}y^{2}} + {A_{14}y^{4}} + {A_{16}x^{4}y} + {A_{18}x^{2}y^{3}} + {A_{20}y^{5}}}},$wherein, c₁ is curvature; k is conic constant; A₂, A₃, A₅, A₇, A₉, A₁₀,A₁₂, A₁₄, A₁₆, A₁₈ and A₂₀ are coefficients. In one embodiment, valuesof the curvature c₁, conic constant k, and the coefficients A₂, A₃, A₅,A₇, A₉, A₁₀, A₁₂, A₁₄, A₁₆, A₁₈ and A₂₀ are listed in table 1.

TABLE 1 c₁ −0.00840342361559533 k −13.1593092531843 A₂−5.52278890932116E−14 A₃ 2.96489354878911E−03 A₅ 2.91326939497068E−03 A₇4.76838525024617E−08 A₉ 7.82131155179962E−08 A₁₀ 6.19731744269913E−07A₁₂ −1.27490547215523E−08 A₁₄ −1.79954964051450E−07 A₁₆−2.11928233145496E−08 A₁₈ −8.66202887985918E−10 A₂₀ 9.97940014815302E−10

The second freeform surface 1624 can be a 5^(th) order XY-polynomialcurve surface. In some embodiments, an analytic form of the secondfreeform surface 1624 satisfies:

${{z\left( {x,y} \right)} = {\frac{c_{2}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c_{2}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}^{\prime}y} + {A_{3}^{\prime}x^{2}} + {A_{5}^{\prime}y^{2}} + {A_{7}^{\prime}x^{2}y} + {A_{9}^{\prime}y^{3}} + {A_{10}^{\prime}x^{4}} + {A_{12}^{\prime}x^{2}y^{2}} + {A_{14}^{\prime}y^{4}} + {A_{16}^{\prime}x^{4}y} + {A_{18}^{\prime}x^{2}y^{3}} + {A_{20}^{\prime}y^{5}}}},$wherein, c₂ is curvature; k′ is conic constant; A′₂, A′₃, A′₅, A′₇, A′₉,A′₁₀, A′₁₂, A′₁₄, A′₁₆, A′₁₈ and A′₂₀ are coefficients. In oneembodiment, values of the curvature c₂, conic constant k′, and thecoefficients A′₂, A′₃, A′₅, A′₇, A′₉, A′₁₀, A′₁₂, A′₁₄, A′₁₆, A′₁₈ andA′₂₀ are listed in table 2.

TABLE 2 c₂ −0.00840342361559533 K′ −13.1593092531843 A′₂5.52278890932116E−14 A′₃ 2.96489354878911E−03 A′₅ 2.91326939497068E−03A′₇ −4.76838525024617E−08 A′₉ −7.82131155179962E−08 A′₁₀6.19731744269923E−07 A′₁₂ −1.27490547215523E−08 A′₁₄−1.79954964051450E−07 A′₁₆ 2.11928233145496E−08 A′₁₈8.66202887985918E−10 A′₂₀ −9.97940014815302E−10

The back surface 164 can be a 10^(th) order aspheric surface. In someembodiments, an analytic form of the back surface 164 satisfies:

${{z\left( {x,y} \right)} = {\frac{c_{3}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k_{1}} \right){c_{3}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {D\left( {x^{2} + y^{2}} \right)}^{2} + {E\left( {x^{2} + y^{2}} \right)}^{3} + {F\left( {x^{2} + y^{2}} \right)}^{4} + {G\left( {x^{2} + y^{2}} \right)}^{5}}},$wherein, c₃ is curvature; k₁ is conic constant; D, E, F, and G arecoefficients. In one embodiment, values of the curvature c₃, conicconstant k₁, and the coefficients D, E, F, and G are listed in table 3.

TABLE 3 c₃ 0.00796808853571445 K₁ 0.637349059540081 D

1.42634797718698E−07 E −8.51981255927027E−12 F 9.81455629012912E−16 G−1.30179502542930E−19

The image sensing element 18 is located on a light path of the refractedlight T, and is parallel to a x-y plane. An effective scanning range R₃of the image sensing element 18 along the y-axis is greater than 420millimeters. In one embodiment, the effective scanning range R₃ of theimage sensing element 18 along the y-axis is about 420 millimeters.

Referring to FIG. 3, when the reflector 14 revolves around the center O₁from about 15 degrees to about 75 degrees, a linear scan with a filedangle θ from about −60 degrees to about +60 degrees can be achieved.Referring to FIG. 4, a scanning error of the filed angle θ from about−60 degrees to about 60 degrees on the image sensing element 18 iswithin ±1 micron. Referring to FIGS. 5-8, according to the MTF curves ofthe freeform imaging system 100, the freeform imaging system 100 withall filed angles can reach a diffraction limit. Thus, the freeformimaging system has a superior performance in imaging. Furthermore, thefreeform imaging system comprises only one freeform imaging lens, and iseasy to be assembled.

It is to be understood that the above-described embodiments are intendedto illustrate rather than limit the disclosure. Any elements describedin accordance with any embodiments is understood that they can be usedin addition or substituted in other embodiments. Embodiments can also beused together. Variations may be made to the embodiments withoutdeparting from the spirit of the disclosure. The above-describedembodiments illustrate the scope of the disclosure but do not restrictthe scope of the disclosure.

What is claimed is:
 1. A freeform imaging lens, defined in a (x,y,z)coordinate, comprising: a first surface and a second surface opposite tothe first surface, wherein the first surface comprises a first freeformsurface and a second freeform surface that are symmetrical about an x-zplane, the first freeform surface and the second freeform surface areboth 5^(th) order xy-polynomial curve surfaces, and the second surfaceis a 10^(th) order aspheric surface, wherein an analytic form of thefirst freeform surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{1}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c_{1}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}y} + {A_{3}x^{2}} + {A_{5}y^{2}} + {A_{7}x^{2}y} + {A_{9}y^{3}} + {A_{10}x^{4}} + {A_{12}x^{2}y^{2}} + {A_{14}y^{4}} + {A_{16}x^{4}y} + {A_{18}x^{2}y^{3}} + {A_{20}y^{5}}}},$wherein, c₁ is curvature of the first freeform surface; k is a conicconstant; A₂, A₃, A₅, A₇, A₉, A₁₀, A₁₂, A₁₄, A₁₆, A₁₈ and A₂₀ arecoefficients.
 2. The freeform imaging lens of claim 1, wherein values ofthe curvature c₁, the conic constant k, and the coefficients A₂, A₃, A₅,A₇, A₉, A₁₀, A₁₂, A₁₄, A₁₆, A₁₈ A₂₀ are listed as following: c₁−0.00840342361559533 k −13.1593092531843 A₂ −5.52278890932116E−14 A₃2.96489354878911E−03 A₅ 2.91326939497068E−03 A₇ 4.76838525024617E−08 A₉7.82831155179962E−08 A₁₀ 6.19731744269923E−07 A₁₂ −1.27490547215523E−08A₁₄ −1.79954964051450E−07 A₁₆ −2.11928233145496E−08 A₁₈−8.66202887985918E−10 A₂₀ 9.97940014815302E−10.


3. The freeform imaging lens of claim 1, wherein an analytic form of thesecond freeform surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{2}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c_{2}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}^{\prime}y} + {A_{3}^{\prime}x^{2}} + {A_{5}^{\prime}y^{2}} + {A_{7}^{\prime}x^{2}y} + {A_{9}^{\prime}y^{3}} + {A_{10}^{\prime}x^{4}} + {A_{12}^{\prime}x^{2}y^{2}} + {A_{14}^{\prime}y^{4}} + {A_{16}^{\prime}x^{4}y} + {A_{18}^{\prime}x^{2}y^{3}} + {A_{20}^{\prime}y^{5}}}},$wherein, c₂ is curvature; k′ is conic constant; A′₂, A′₃, A′₅, A′₇, A′₉,A′₁₀, A′₁₂, A′₁₄, A′₁₆, A′₁₈ and A′₂₀ are coefficients.
 4. The freeformimaging lens of claim 3, wherein values of the curvature c₂, conicconstant k′, and the coefficients A′₂, A′₃, A′₅, A′₇, A′₉, A′₁₀, A′₁₂,A′₁₄, A′₁₆, A′₁₈ and A′₂₀ are listed as following: c₂−0.00840342361559533 K′ −13.1593092531843 A′₂ 5.52278890932116E−14 A′₃2.96489354878911E−03 A′₅ 2.91326939497068E−03 A′₇ −4.76838525024617E−08A′₉ −7.82131155179962E−08 A′₁₀ 6.19731744269923E−07 A′₁₂−1.27490547215523E−08 A′₁₄ −1.79954964051450E−07 A′₁₆2.11928233145496E−08 A′₁₈ 8.66202887985918E−10 A′₂₀−9.97940014815302E−10.


5. The freeform imaging lens of claim 1, wherein an analytic form of thesecond surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{1}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k_{1}} \right){c_{1}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {D\left( {x^{2} + y^{2}} \right)}^{2} + {E\left( {x^{2} + y^{2}} \right)}^{3} + {F\left( {x^{2} + y^{2}} \right)}^{4} + {G\left( {x^{2} + y^{2}} \right)}^{5}}},$wherein, c₃ is curvature; k₁ is conic constant; D, E, F, and G arecoefficients.
 6. The freeform imaging lens of claim 5, wherein values ofthe curvature c₃, conic constant k₁, and the coefficients D, E, F, G arelisted as following: c₃ 0.00796808853571445 K₁ 0.637349059540081 D

1.42634797718698E−07 E −8.51981255927027E−12 F 9.81455629012912E−16 G−1.30179502542930E−19.


7. A freeform imaging system, defined in a (x, y, z) coordinate,comprising: a light source outputting a laser along a y-axis; anentrance pupil located on a light path of the laser; a reflectorperpendicular to a y-z plane located on a side of the entrance pupilopposite to the light source and configured to reflect the laser to forma reflected light in the y-z plane, wherein the reflector has a centerand is capable of revolve around the center; a freeform imaging lenslocated on a light path of the reflected light comprising a frontsurface and a back surface opposite to the front surface, wherein thereflected light is refracted by the freeform imaging lens to form arefracted light, the front surface comprises a first freeform surfaceand a second freeform surface that are symmetrical about an x-z plane,the first freeform surface and the second freeform surface are both5^(th) order xy-polynomial curve surfaces, and the back surface is a10^(th) order aspheric surface; and an image sensing element, parallelto a x-y plane, located on a light path of the refracted light, whereinan analytic form of the first freeform surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{1}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k} \right){c_{1}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}y} + {A_{3}x^{2}} + {A_{5}y^{2}} + {A_{7}x^{2}y} + {A_{9}y^{3}} + {A_{10}x^{4}} + {A_{12}x^{2}y^{2}} + {A_{14}y^{4}} + {A_{16}x^{4}y} + {A_{18}x^{2}y^{3}} + {A_{20}y^{5}}}},$wherein, c₁ is curvature; k is conic constant; A₂, A₃, A₅, A₇, A₉, A₁₀,A₁₂, A₁₄, A₁₆, A₁₈ and A₂₀ are coefficients.
 8. The freeform imagingsystem of claim 7, wherein values of the curvature c₁, the conicconstant k, and the coefficients A₂, A₃, A₅, A₇, A₉, A₁₀, A₁₂, A₁₄, A₁₆,A₁₈ A₂₀ are listed as following: c₁ −0.00840342361559533 k−13.1593092531843 A₂ −5.52278890932116E−14 A₃ 2.96489354878911E−03 A₅2.91326939497068E−03 A₇ 4.76838525024617E−08 A₉ 7.82131155179962E−08 A₁₀6.19731711269923E−07 A₁₂ −1.27490547215523E−08 A₁₄ −1.79954964051450E−07A₁₆ −2.11928233145496E−08 A₁₈ −8.66202887985918E−10 A₂₀9.97940014815302E−10.


9. The freeform imaging system of claim 7, wherein an analytic form ofthe second freeform surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{2}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k^{\prime}} \right){c_{2}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {A_{2}^{\prime}y} + {A_{3}^{\prime}x^{2}} + {A_{5}^{\prime}y^{2}} + {A_{7}^{\prime}x^{2}y} + {A_{9}^{\prime}y^{3}} + {A_{10}^{\prime}x^{4}} + {A_{12}^{\prime}x^{2}y^{2}} + {A_{14}^{\prime}y^{4}} + {A_{16}^{\prime}x^{4}y} + {A_{18}^{\prime}x^{2}y^{3}} + {A_{20}^{\prime}y^{5}}}},$wherein, c₂ is curvature; k′ is conic constant; A′₂, A′₃, A′₅, A′₇, A′₉,A′₁₀, A′₁₂, A′₁₄, A′₁₆, A′₁₈ and A′₂₀ are coefficients.
 10. The freeformimaging system of claim 9, wherein values of the curvature c₂, conicconstant k′, and the coefficients A′₂, A′₃, A′₅, A′₇, A′₉, A′₁₀, A′₁₂,A′₁₄, A′₁₆, A′₁₈ and A′₂₀ are listed as following: c₂−0.00840342361559533 K′ −13.1593092531843 A′₂ 5.52278890932116E−14 A′₃2.96489354878911E−03 A′₅ 2.91326939497068E−03 A′₇ −4.76838525024617E−08A′₉ −7.82131155179962E−08 A′₁₀ 6.19731744269923E−07 A′₁₂−1.27490547215523E−08 A′₁₄ −1.79954961051450E−07 A′₁₆2.11928233145496E−08 A′₁₈ 8.66202887985918E−10 A′₂₀−9.97940014815302E−10.


11. The freeform imaging system of claim 7, wherein an analytic form ofthe back surface satisfies:${{z\left( {x,y} \right)} = {\frac{c_{1}\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {\left( {1 + k_{1}} \right){c_{1}^{2}\left( {x^{2} + y^{2}} \right)}}}} + {D\left( {x^{2} + y^{2}} \right)}^{2} + {E\left( {x^{2} + y^{2}} \right)}^{3} + {F\left( {x^{2} + y^{2}} \right)}^{4} + {G\left( {x^{2} + y^{2}} \right)}^{5}}},$wherein, c₃ is curvature; k₁ is conic constant; D, E, F, and G arecoefficients.
 12. The freeform imaging system of claim 11, whereinvalues of the curvature c₃, conic constant k₁, and the coefficients D,E, F, G are listed as following: c₃ 0.00796808853571445 K₁0.637349059540081 D

1.42634797718698E−07 E −8.51981255927027E−12 F 9.81455629012912E−16 G−1.30179502542930E−19.


13. The freeform imaging system of claim 7, wherein an angle α formedbetween the reflector and the y-axis is in a range from about 15 degreesto about 75 degrees.
 14. The freeform imaging system of claim 7, whereina width of the laser with a wavelength of about 780 nanometers is about3 millimeters.
 15. The freeform imaging system of claim 7, wherein amaterial of the freeform imaging lens is PMMA with a refractive index ofabout 1.4917 and an Abbe number of about
 76. 16. The freeform imagingsystem of claim 7, wherein a filed angle of the freeform imaging systemranges from about −60 degrees to about +60 degrees.